Analysis and applications of the exponential time differencing schemes and their contour integration modifications

被引：99

作者：

Du, Q ^{[1
]}

Zhu, WX ^{[1
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

来源：

BIT NUMERICAL MATHEMATICS | 2005年 / 45卷 / 02期

关键词：

time integration schemes; exponential time differencing; contour integrals; Fourier spectral methods; stability; Fourier analysis; energy estimates; maximum principle; Allen-Cahn equations; phase transitions;

D O I：

10.1007/s10543-005-7141-8

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We study in this paper the exponential time differencing (ETD) schemes and their modifications via complex contour integrations for the numerical solutions of parabolic type equations. We illustrate that the contour integration shares an added advantage of improving the stability of the time integration. In addition, we demonstrate the effectiveness of the ETD type schemes through the numerical solution of a typical problem in phase field modeling and through the comparisons with other existing methods.

引用

页码：307 / 328

页数：22

共 50 条

[21] Exponential time differencing FDTD formulation for plasma
Huang, Sh. J.
MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, 2007, 49 (06) : 1363 - 1364
[22] Exponential Time Differencing Schemes for the Peng-Robinson Equation of State with Preservation of Maximum Bound Principle
Huang, Qiumei
Jiang, Kun
Li, Jingwei
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2022, 14 (02) : 494 - 527
[23] TIME-DIFFERENCING SCHEMES AND TRANSFORM METHODS
GAZDAG, J
JOURNAL OF COMPUTATIONAL PHYSICS, 1976, 20 (02) : 196 - 207
[24] Exponential time integration and Chebychev discretisation schemes for fast pricing of options
Tangman, D. Y.
Gopaul, A.
Bhuruth, M.
APPLIED NUMERICAL MATHEMATICS, 2008, 58 (09) : 1309 - 1319
[25] Quantifying and eliminating the time delay in stabilization exponential time differencing Runge-Kutta schemes for the Allen-Cahn equation
Zhang, Hong
Liu, Lele
Qian, Xu
Song, Songhe
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 2024, 58 (01) : 191 - 221
[26] ENERGY STABILITY AND ERROR ESTIMATES OF EXPONENTIAL TIME DIFFERENCING SCHEMES FOR THE EPITAXIAL GROWTH MODEL WITHOUT SLOPE SELECTION
Ju, Lili
Li, Xiao
Qiao, Zhonghua
Zhang, Hui
MATHEMATICS OF COMPUTATION, 2018, 87 (312) : 1859 - 1885
[27] Note on Filon-type integration for higher order exponential time differencing methods in stiff systems
Xiang, SH
JOURNAL OF CENTRAL SOUTH UNIVERSITY OF TECHNOLOGY, 2005, 12 (Suppl 1): : 298 - 303
[28] An exponential time differencing method for the nonlinear Schrodinger equation
de la Hoz, F.
Vadillo, F.
COMPUTER PHYSICS COMMUNICATIONS, 2008, 179 (07) : 449 - 456
[29] Exponential time differencing algorithm for Debye medium in FDTD
Huang, Sh. J.
INTERNATIONAL JOURNAL OF INFRARED AND MILLIMETER WAVES, 2007, 28 (11): : 1025 - 1031
[30] Note on filon-type integration for higher order exponential time differencing methods in stiff systems
Shu-huang Xiang
Journal of Central South University of Technology, 2005, 12 : 298 - 303

← 1 2 3 4 5 →